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Showing 1 to 6 of 6 for “"complementary prism"”.
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Induced path number for the complementary prism of a grid graph
… so that each subset induces a path. A complementary prism of a graph G that we will refer to as CP(G) is the graph formed from the disjoint union of G and G_bar and adding the edges between the corresponding vertices of G and G_bar. These new edges are called prism edges. The graph …
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Restrained and Other Domination Parameters in Complementary Prisms.
… parameters of a family of graphs known as complementary prisms. We will first present the basic terminology and definitions necessary to understand the topic. Then, we will examine the known results addressing the domination number and the total domination number of complementary prisms. …
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The induced path number of complementary prisms
The complementary prism GG of a graph G is formed from the disjoint union of G and its complement G by adding the edges of a perfect matching between the corresponding vertices of G and G. The induced path number, denoted ρ(G), of a graph G is defined as the minimum number of subsets that the …
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Independent Domination in Complementary Prisms.
… <em>G̅</em> be the complement of <em>G</em>. The complementary prism <em>GG̅</em> of <em>G</em> is the graph formed from the disjoint union of <em>G</em> and <em>G̅</em> by adding the edges of a perfect matching between the corresponding vertices of <em>G</em> and <em>G̅</em>. For example, if …
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Double Domination of Complementary Prisms.
<p>The complementary prism of a graph <em>G</em> is obtained from a copy of <em>G</em> and its complement <em>G̅</em> by adding a perfect matching between the corresponding vertices of <em>G</em> and <em>G̅</em>. For any graph <em>G</em>, a set <em>D</em> ⊆ <em>V</em> (<em>G</em>) is a <em>double …
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Locating-Domination in Complementary Prisms.
… <em>G̅</em> be the complement of <em>G</em>. The complementary prism of <em>G</em>, denoted <em>GG̅</em>, is the graph formed from the disjoint union of <em>G</em> and <em>G̅</em> by adding the edges of a perfect matching between the corresponding vertices of <em>G</em> and <em>G̅</em>. A set …